11 15 17 triangle

Acute scalene triangle.

Sides: a = 11   b = 15   c = 17

Area: T = 81.26599993847
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 39.59332587094° = 39°35'36″ = 0.69110327261 rad
Angle ∠ B = β = 60.35331677636° = 60°21'11″ = 1.05333614915 rad
Angle ∠ C = γ = 80.0543573527° = 80°3'13″ = 1.3977198436 rad

Height: ha = 14.77545453427
Height: hb = 10.83546665846
Height: hc = 9.56599999276

Median: ma = 15.05882203464
Median: mb = 12.19663109177
Median: mc = 10.03774299499

Inradius: r = 3.78795348551
Circumradius: R = 8.63297071783

Vertex coordinates: A[17; 0] B[0; 0] C[5.44111764706; 9.56599999276]
Centroid: CG[7.48803921569; 3.18766666425]
Coordinates of the circumscribed circle: U[8.5; 1.49105857853]
Coordinates of the inscribed circle: I[6.5; 3.78795348551]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.4076741291° = 140°24'24″ = 0.69110327261 rad
∠ B' = β' = 119.6476832236° = 119°38'49″ = 1.05333614915 rad
∠ C' = γ' = 99.9466426473° = 99°56'47″ = 1.3977198436 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 11 ; ; b = 15 ; ; c = 17 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 11+15+17 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-11)(21.5-15)(21.5-17) } ; ; T = sqrt{ 6603.19 } = 81.26 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.26 }{ 11 } = 14.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.26 }{ 15 } = 10.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.26 }{ 17 } = 9.56 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 11**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 39° 35'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-17**2 }{ 2 * 11 * 17 } ) = 60° 21'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 80° 3'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.26 }{ 21.5 } = 3.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 39° 35'36" } = 8.63 ; ;




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